The Nigeria international has been absent for Chelsea's past four matches with the complaint, including Sunday's 2-0 victory over Tottenham in the League Cup final.
Manager Jose Mourinho has subsequently confirmed that Mikel has had an operation to correct the issue and expects him to be absent until April.
"Mikel had a little surgery on his meniscus," he said.
"We are expecting him to be out for about a month, one week is already gone, there is not too much optimism or pessimim.
"I would say [he will return] first week of April."
Mikel is now likely to miss the Premier League matches against West Ham, Southampton and Hull City as well as the UEFA Champions League last-16 second-leg tie at home to Paris Saint-Germain.
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